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Rigged configurations are known to provide action-angle variables for remarkable discrete dynamical systems known as box-ball systems. We conjecture an explicit piecewise-linear formula to obtain the shapes of a rigged configuration from a…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Let $X$ be an integrable real random variable with mean zero and two-sided sub-Gaussian tail $\mathbb{P}(|X|>t)\le 2e^{-t^{2}/2}$ for all $t\ge 0$. We determine the smallest constant $c_\star$ such that $X$ is dominated in convex order by…
It was shown by G. Pisier that any finite-dimensional normed space admits an $\alpha$-regular $M$-position, guaranteeing not only regular entropy estimates but moreover regular estimates on the diameters of minimal sections of its unit-ball…
We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…
A result of Bangert states that the stable norm associated to any Riemannian metric on the $2$-torus $T^2$ is strictly convex. We demonstrate that the space of stable norms associated to metrics on $T^2$ forms a proper dense subset of the…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
A general study of relations between the parameters of two centrally-symmetric Levy distributions, often used for one-dimensional investigation of Bose - Einstein correlations, is given for the first time. These relations of the strength of…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that during the interaction of solitons of the same signs the wave field is effectively smoothed out. When the…
According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is $C^{1,1}$ around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present…
Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…
A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…